Drag the locators to move the lines. Each locator snaps to the nearest point with integer coordinates. The equations of the lines are displayed on the right as a two-by-two system of linear equations with integer coefficients. Provided that a unique solution exists, it will be displayed as well (the solution is the point of intersection of the two lines).
It is not hard to position the lines in such a way that the solution will also be a point with integer coordinates. This Demonstration can be used to generate thousands of such examples. Mathematics instructors can use it as a simple tool for creating problems for beginning students.
You can also use it to challenge more advanced students; for example, among all systems that can be generated here whose solution has integer coordinates, can you find one whose solution is farthest from the origin?